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Ecology, 93(6), 2012, pp. 1482–1487
! 2012 by the Ecological Society of America
Niche and fitness differences relate
the maintenance of diversity to
ecosystem function: comment
MICHEL LOREAU,1,2,6 JURGIS SAPIJANSKAS,1,3
FOREST ISBELL,1,4 AND ANDY HECTOR5
The relationship between biodiversity and ecosystem
functioning (BEF) has been one of the most vibrant
research fields in ecology and environmental sciences
over the past two decades. Hundreds of experiments
have now manipulated species diversity to test its effects
on a wide range of ecosystem properties. Methods that
partition the effect of functional complementarity
between species from that of selection for species with
particular traits have been instrumental in clarifying the
results of these experiments and in resolving debates
about potential underlying mechanisms (Loreau and
Hector 2001, Cardinale et al. 2007). Relatively few
studies, however, have sought to disentangle the actual
biological mechanisms at work in the effects of
biodiversity on ecosystem functioning. Yet theory shows
that different coexistence mechanisms can lead to
different BEF relationships (Mouquet et al. 2002).
Understanding the mechanisms that drive the functional
consequences of biodiversity and their connections with
those that determine the maintenance of biodiversity is
key to making BEF research more predictive and more
relevant to natural, non-experimentally manipulated
ecosystems (Loreau 2010).
The recent theoretical study by Carroll, Cardinale,
and Nisbet (2011; hereafter CCN) makes a valuable
contribution toward the goal of linking the maintenance
Manuscript received 13 May 2011; revised 5 October 2011;
accepted 7 October 2011. Corresponding Editor: S. J. Schreiber.
1 Department of Biology, McGill University, 1205 avenue
Docteur Penfield, Montreal, Quebec H3A 1B1 Canada.
2 Centre for Biodiversity Theory and Modelling, Experimental Ecology Station, Centre National de la Recherche
Scientifique, 09200 Moulis, France.
3 AgroParisTech ENGREF, 19 avenue du Maine, 75015
Paris, France.
4 Department of Ecology, Evolution and Behavior, University of Minnesota, 1987 Upper Buford Circle, Saint Paul,
Minnesota 55108 USA.
5 Institute of Evolutionary Biology and Environmental
Studies, University of Zürich, Winterthurerstrasse 190, 8057
Zürich, Switzerland.
6 E-mail: [email protected]
of diversity and its functional consequences. CCN use
MacArthur’s (1972) classical consumer!resource model
to develop new measures of niche difference (ND) and
relative fitness difference (RFD) between consumers.
They then explore the relationships between these new
measures and the widely used additive partition (AP) of
the net biodiversity effect into a complementarity effect
(CE) and a selection effect (SE), as well as the relative
yield total (RYT), a measure closely related to CE
(Loreau and Hector 2001). Their analysis leads them to
conclude that ‘‘post hoc statistical methods currently
used to discern the mechanisms that drive effects of
diversity on biomass do not necessarily reflect real
biological processes that relate to mechanisms of species
coexistence.’’ This conclusion serves as a reminder that,
however useful, no post hoc analysis will ever be able to
replace detailed knowledge of the biological mechanisms
at work.
But CCN also suggest that the ND and RFD metrics
they devise are more appropriate than AP for identifying mechanisms that drive BEF relationships; accordingly, they propose that future theoretical and
empirical work should focus on ‘‘predicting community
biomass from three independent variables: ND, RFD,
and species richness.’’ As we explain here, we feel that
these additional conclusions are unwarranted; they are
based on the implicit assumption that CCN’s new
approach is intrinsically better than AP without any
independent demonstration that it does in fact do a
better job. On the other hand, CCN’s study raises valid
questions about the scope and limitations of AP, which
has been sometimes liberally interpreted in the recent
literature. In this comment, therefore, we would like to
(1) revisit the scope and limitations of the AP approach,
(2) discuss some of the limitations of CCN’s new
proposed approach, and (3) briefly suggest some
directions that could be taken to move BEF research
forward.
When two of us proposed AP 10 years ago (Loreau
and Hector 2001), it was in the context of a raging
debate about the interpretation of BEF experiments
(Loreau et al. 2001). The main interest of this approach
was to allow testing of hypotheses that assume changes
in numerical dominance among species but no functional complementarity, such as the much-debated ‘‘sampling effect’’ and ‘‘mass ratio’’ hypotheses. Essentially,
these hypotheses propose that changes in community
production or biomass can be explained simply by zerosum changes in the relative abundances of species in
mixture. The alternative, that communities are more (or
less) than the sum of their parts, has for a long time been
termed overyielding (or underyielding). AP has played a
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COMMENTS
valuable role for testing these types of null hypothesis
via its two components, SE and CE.
SE is a straightforward application of a basic
statistical approach: it is a covariance term that relates
the performance of a species in mixture (whether its
relative yield increases or decreases relative to expectations) to its monoculture biomass. It is positive when
species with large monoculture biomasses on average
perform better in mixtures, and negative when the
reverse is true. When changes in relative abundances
follow a zero-sum game, then SE (whatever its sign) will
explain the effects of diversity on mixture yield.
Ecologists are familiar with covariances and correlations; thus SE is relatively simple and easy to
understand.
CE quantifies overyielding, i.e., an increase in mixture
yield above the zero-sum expectation (or underyielding
when mixtures produce less than expected), which
provides a simple, operational way to define functional
complementarity by its net effect at the community level.
Although technically CE has the dimension of absolute
yield, one advantage is that it is closely related to the
relative yield and RYT concepts used in plant ecology
and intercropping since the 1950s and they are therefore
once again familiar to ecologists and relatively well
understood. In addition, CE and RYT have the nice
property of being directly connected to the conditions
for stable coexistence in the classical Lotka-Volterra
competition model (Vandermeer 1981, Loreau 2004).
In total, the AP and RYT frameworks are relatively
simple and based on long-established methodologies
that are familiar to many ecologists. We therefore feel
that, despite their limitations, they will continue to have
great value for performing tests of null hypotheses such
as the sampling effect and mass ratio hypotheses, and
for generating alternative hypotheses about possible
mechanisms underlying BEF relationships detected in
experiments.
It is important to note, however, that CE and RYT do
not provide quantitative measures of resource partitioning because they potentially combine the effects of a
wide range of species interactions, as one of us
established clearly (Loreau 1998). A positive CE (or,
equivalently, RYT . 1) means that niche differentiation
(partitioning of either resources or natural enemies),
positive interactions, or some combination thereof, are
strong enough to outweigh interference competition or
other negative species interactions that might decrease
relative yields in mixture. Conversely, a negative CE (or
RYT , 1) indicates that negative species interactions are
strong enough to outweigh the positive effects of niche
differentiation and positive interactions on relative
yields in mixture. Thus, AP was devised as a tool to
test hypotheses, not as a tool to identify the type and
strength of species interactions. It is the sign and relative
magnitude of CE and SE that matter in hypothesis
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testing, while their absolute magnitudes should be
interpreted more cautiously because of the range of
biological processes that can affect them.
Liberal interpretations of AP as a means to identify
and quantify species interactions may have resulted
from ambiguous usage of the term ‘‘mechanism’’ in the
BEF literature as well as in other areas of ecology. A
‘‘mechanism’’ denotes any lower-level process that
contributes to generating a higher-level ‘‘phenomenon’’
of interest. In this sense, although CE and SE, the two
components of AP, provide information about which
mechanisms are compatible with the observed effects of
biodiversity on ecosystem functioning, they do not
themselves correspond to particular biological mechanisms because they combine the effects of a potentially
wide range of individual-level processes on the community-level phenomenon of yield, hence their appropriate
designation as ‘‘effects.’’ The literature, however (including Loreau and Hector 2001), has often used the
terms ‘‘mechanisms,’’ ‘‘classes of mechanisms,’’ or ‘‘types
of mechanisms’’ to describe CE and SE, leading
sometimes to the improper interpretation that they
quantify individual-level biological processes. Just as
with any other approach, greater terminological and
conceptual clarity is likely to help better appreciate the
scope and limitations of AP.
The new approach proposed by CCN relies on an
attempt to formalize Chesson’s (2000) conceptual
distinction between stabilizing and equalizing coexistence ‘‘mechanisms.’’ They build measures of ND and
RFD that capture these two ‘‘mechanisms’’ based on
the sensitivities of species’ invasion rates to interspecific
competition. Specifically, ND is measured as one minus
the geometric mean of these sensitivities, while RFD is
measured as their geometric standard deviation. CCN
then show that both increasing ND and decreasing
RFD increases RYT and CE, in contrast to their
intuitive expectations that only ND should affect RYT
and CE based on the assumption that the latter
measure resource partitioning between species. This
particular result leads them to conclude that current
measures of functional complementarity ‘‘give a largely
skewed estimate of resource partitioning.’’ There are,
however, several fundamental problems with this
interpretation.
The first problem follows directly from the above
discussion of the concept of ‘‘mechanism.’’ While
Chesson’s distinction is useful to identify two types of
constraints that affect coexistence, we know of no
evidence that these constraints reflect independent
biological processes, and hence that they correspond
to distinct biological mechanisms. Just as with CE and
SE, the so-called stabilizing and equalizing ‘‘mechanisms’’ define effects at the community level (specifically, on coexistence); these effects also summarize a wide
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COMMENTS
range of species interactions, including resource partitioning, natural enemy partitioning, facilitation, and
interference. Even in the specific context of consumerresource interactions considered by CCN, deterministic
niche differences between species include differences in
niche height (absolute level of resource consumption),
niche breadth, and niche overlap. Differences in niche
height and niche breadth are usually implicitly related to
RFD, while low niche overlap is usually associated with
ND (despite the fact that niche overlap is only one
component of niche differences) because it is a necessary
condition for stable coexistence. Differences in niche
height and niche breadth, however, also affect quantitative measures of niche overlap and the amount of
niche overlap that is necessary to allow coexistence.
Therefore, except in special cases, ND and RFD should
be expected to reflect the operation of a number of
overlapping lower-level processes. Thus, our first
conclusion is that AP and the distinction between
stabilizing and equalizing ‘‘mechanisms,’’ or, more
appropriately, effects, are two alternative ways to sort
the community-level effects of individual-level mechanisms.
A second conclusion follows immediately from the
first. Since the two alternative frameworks provide
different ways to define and aggregate the communitylevel consequences of individual-level processes and
since they work with different quantities (sensitivity of
invasion rates to interspecific competition vs. yield), it is
hardly surprising that they produce different results. The
fact that both ND and RFD affect CE and SE can be no
more an argument for rejecting the latter than the
reciprocal fact that both CE and SE affect ND and RFD
would be an argument for rejecting ND and RFD.
Therefore, without some independent confirmation,
CCN’s results neither justify their suggestion that ND
and RFD are more appropriate than AP for identifying
mechanisms that drive the BEF relationships, nor do
they support their claim that CE gives a skewed estimate
of resource partitioning.
This brings us to a third issue: the specific limitations
of the ND and RFD metrics within the context of BEF
research. In contrast to AP, which was tailored to test
hypotheses about the effects of biodiversity on yield,
ND and RFD bear no necessary relation to yield and
other ecosystem properties that are measured in
biodiversity experiments. The simple relationships that
are often assumed between community-level resource
depletion, production, and biomass at equilibrium hold
only under restricted conditions that may apply to
annual plants but not necessarily to other organisms
(Loreau 2010). The connections between these equilibrium properties and the sensitivity of species’ invasion
rates to interspecific competition are bound to be even
weaker because the traits that govern a species’ ability to
Ecology, Vol. 93, No. 6
invade a subset of a community are not necessarily the
same as those that govern its yield once established in
the full community. There is mounting evidence that the
strength of trophic interactions depends on the presence
and density of other species and that these trophic
interaction modifications themselves interact (Golubski
and Abrams 2011), generating a plethora of higherorder density-dependent effects in communities. For
instance, Bogran et al. (2002) demonstrated phenotypic
plasticity in host use by parasitoids along two niche
axes, such that parasitoid species that appear redundant
when studied independently may become complementary when they coexist. In such cases, niche differences
measured using invasion rates have little to do with
overyielding detected in biodiversity experiments. Experimental evidence also suggests that both the magnitude and the nature of biodiversity effects may change
over time (Cardinale et al. 2007). Thus, while sensitivities of invasion rates are useful within the context of
coexistence theory, it is doubtful that they will generally
provide robust predictors of equilibrium ecosystem
properties. It is also unclear how ND and RFD can be
used to test some of the basic hypotheses of interest in
BEF research. For instance, the sampling effect hypothesis assumes specifically that the species with the highest
monoculture yield or carrying capacity outcompetes the
others in mixtures. ND and RFD are unable to test this
hypothesis because, contrary to SE, they are insensitive
to the ranking of species’ carrying capacities (Appendix
A). For all these reasons, it seems to us that the AP
approach has a distinct practical advantage for hypothesis testing in biodiversity experiments.
Last, the results reported by CCN are largely
restricted to two-species systems, with some additional
simulations for three and four species. Although the
general trends they reveal seem to be robust, they should
not mask some significant deviations from these trends,
which confirm that ND and RFD bear no simple
relations to overyielding, and hence that their use as
tools to interpret biodiversity experiments would require
more careful examination. In particular, CCN’s central
result that RYT (and hence CE) increases as ND
increases and as RFD decreases does not always hold,
even within the restricted scope of MacArthur’s model.
For some scenarios and parameter values, opposite
patterns can be found.
To illustrate and understand this possibility, we use
the continuous formulation of MacArthur’s model
because it provides an explicit measure of niche
differences (sensu niche overlap) between species along
a resource gradient (Sapijanskas and Loreau 2010), and
we focus on the specific example of four consumer
species distributed in two functional groups. For
simplicity, we assume that the two species in each
functional group i have the same niche width, ri, and
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COMMENTS
1485
that the two functional groups are different enough (i.e.,
are spread out enough along the resource gradient) that
competitive interactions between groups is negligible. In
this case, ND, RFD, and RYT can be obtained
analytically (Appendix B):
#
!
"$
1 D21 D22
þ
ð1Þ
ND ¼ 1 ! exp !
8 r21 r22
RFD
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi"ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi#ffiffi9
8 v
!
"2 !
"2 =
<1 u
u!D2 D2 "2
t 1 ! 2 þ32 log K1a þ log K2a
¼ exp
:8
;
K1b
K2b
r21 r22
ð2Þ
!
"!
"
D2
K1a K1b
2 ! exp ! 12
þ
K1b K1a
4r1
RYT ¼
!
"
D21
1 ! exp ! 2
2r1
!
"!
"
D2
K2a K2b
2 ! exp ! 22
þ
K2b K2a
4r2
þ
!
"
D2
1 ! exp ! 22
2r2
ð3Þ
where Kia and Kib are the carrying capacities of the two
species in functional group i, and Di is the distance
between their niche centers along the resource gradient.
As expected, ND decreases exponentially as niche
overlap within functional groups increases (remember
that niche overlap between functional groups is assumed
to be negligible). RFD has two components: the first
term under the square root in Eq. 2 is a measure of the
difference between the two functional groups in the
amount of niche overlap within the group, while the
second is a measure of competitive dominance within the
groups. Note that niche overlap affects both ND and
RFD, such that the two measures are not independent
from each other, as we suggested above based on
intuitive arguments. But niche overlap and competitive
dominance interact more strongly in RYT since the
relative yield total of each functional group weighs the
effect of niche overlap by competitive imbalance such
that decreased niche overlap has a disproportionately
larger positive effect when species are competitively
dissimilar (i.e., when Kia/Kib þ Kia/Kib is larger). Since
RYT incorporates the effects of niche overlap and
competitive imbalance in different ways than do ND
and RFD, all sorts of relationships between these
measures are possible, including relationships that are
opposite to those found by CCN, i.e., RYT can
decrease, rather than increase, as ND increases and as
RFD decreases (Fig. 1). Note that these findings do not
prove that there is anything intrinsically wrong with the
approach based on ND and RFD. But they do challenge
FIG. 1. Changes in the relative yield total, RYT, and the
resulting relationships between RYT and niche difference (ND)
or relative fitness difference (RFD) when niche overlap varies in
a community of four species distributed in two functional
groups (Eqs. 1–3). Niche overlap is here varied in opposite
directions in the two functional groups using the following
transformation:
& 2
'
& 2
'
D1 D22
D1
D2
; 2 !
! d; 22 þ 1:5d
2
2
r1 r2
r1
r2
where d is a nonnegative parameter that allows niche overlap to
vary from the reference situation (in which d ¼ 0). Kia and Kib
are the carrying capacities of the two species in functional
group i, Di is the distance between their niche centers along the
resource gradient, and ri is the niche width of group i.
Parameters were chosen such that there is both greater niche
overlap (D1/r1 , D2/r2) and greater competitive imbalance
(K1a/K1b þ K1b/K1a . K2a/K2b þ K2b/K2a) in the first functional
group. ND and RFD are increasing and decreasing functions,
respectively, of d. Yet, RYT decreases with d because the
competitive imbalance between the two groups is sufficiently
large for the positive effect of reduced niche overlap in the
second group (D22 /r22 þ 1.5d) to overwhelm the negative effect of
increased overlap in the first (D21 /r21 ! d) (Appendix C). In this
example, D21 /r21 ¼ 3, D22 /r22 ¼ 4.5, K2a ¼ K2b, and K1a ¼ 2K1b.
Stable coexistence of the four species requires d , 1.4.
the use of these metrics as some sort of self-evident
reference against which RYT and AP should be
assessed. We see no justification for assuming the
superiority of the first approach over the second.
Where does all this leave the BEF research field?
Methods based on relative yield, in particular AP, have
been the primary tool used in identifying biodiversity
effects over the last 10–15 years. CCN’s study reiterates
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COMMENTS
that CE cannot be directly equated to resource
partitioning, and shows that CE and SE do not
correspond to stabilizing and equalizing coexistence
effects. This is not surprising because CE and SE were
not developed to quantify resource partitioning or
coexistence mechanisms. Instead, CE and SE are useful
tools to test hypotheses. For example, Cardinale (2011)
used AP in the analysis of a recent experiment where SE
and CE appear to do a good job in identifying the
signatures of species dominance and complementarity,
respectively. Unfortunately, the ND and RFD measures
proposed by CCN are also unable to quantify biological
processes such as resource partitioning because, like CE
and SE, they are net measures of multiple biological
processes. Thus, it is unclear how they can contribute to
enhance our ability to detect biological mechanisms.
Given the limitations inherent in all preexisting post
hoc statistical methods (reviewed in Hector et al. 2009)
and CCN’s new approach, how can we make further
progress in understanding the mechanisms that explain
the maintenance of biodiversity and its functional
consequences? We believe that such progress requires
at least two key ingredients. The first is expanding
theory that connects the microscopic mechanics of
species interactions and the macroscopic properties of
whole ecosystems. There have been recent developments
in this area (Loreau 2010), and we welcome CCN’s work
as a new contribution toward this shared goal. The main
challenge for theory development will be to keep a
unifying perspective while examining the mechanistic
details of species interactions. The distinction between
stabilizing and equalizing coexistence effects provides
one possible unifying framework, but others are
conceivable. One of the important roles of ecological
theory should be to build and explore alternative
unifying frameworks that link the microscopic and
macroscopic properties of ecosystems. Second, we need
a new generation of experiments that analyze the
individual- and population-level processes that generate
the effects of biodiversity on ecosystem functioning.
When two of us proposed the AP methodology (Loreau
and Hector 2001), we concluded that this methodology
‘‘cannot replace direct experimental investigations into
the mechanisms at work in responses to biodiversity
changes at the ecosystem level, which are now critical to
further progress in this area.’’ This conclusion is still
topical today. A few pioneering studies have experimentally manipulated available niche space (Dimitrakopoulos and Schmid 2004, Cardinale 2011) or species’ niches
through evolution (Gravel et al. 2011) to test for the role
of resource partitioning in shaping BEF relationships.
Others have manipulated intra- and interspecific population densities simultaneously to disentangle the roles
of niche differences and facilitation in overyielding
(Gross et al. 2007, Northfield et al. 2010). Still others
Ecology, Vol. 93, No. 6
have manipulated the presence of mutualists (van der
Heijden et al. 1998) or pathogens (Maron et al. 2011,
Schnitzer et al. 2011) to test for their role in driving BEF
relationships. But overall the number of studies that
have tested underlying mechanisms explicitly is still too
limited to draw general conclusions on the lower-level
processes that drive BEF relationships and the way these
processes interact. Combining innovative theory and
experiments that allow us to disentangle these processes
and bring them together in a coherent unifying
framework should now be a major research focus in
community and ecosystem ecology.
Acknowledgments
M. Loreau was supported by the Natural Sciences and
Engineering Research Council of Canada and the Canada
Research Chair program. J. Sapijanskas was funded by the
French Ministry of Agriculture. A. Hector was supported by
Microsoft Research as a visiting researcher in computational
ecology and environmental sciences.
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SUPPLEMENTAL MATERIAL
Appendix A
Proof showing that, contrary to the selection effect (SE), niche difference (ND) and relative fitness difference (RFD) are
insensitive to the ranking of carrying capacities in the classical two-species Lotka-Volterra model (Ecological Archives E093-130A1).
Appendix B
MacArthur’s model with four species and two functional groups distributed along a continuous resource gradient (Ecological
Archives E093-130-A2).
Appendix C
Proof that reduced niche overlap has a stronger effect on the relative yield total of functional group i (RYTi) when competitive
imbalance is higher in MacArthur’s model with four species and two functional groups (Ecological Archives E093-130-A3).
_______________________________
Ecology, 93(6), 2012, pp. 1487–1491
! 2012 by the Ecological Society of America
Niche and fitness differences relate
the maintenance of diversity to
ecosystem function: reply
IAN T. CARROLL,1,3 BRADLEY J. CARDINALE,2
ROGER M. NISBET1
AND
Manuscript received 13 May 2011; revised 5 October 2011;
accepted 7 October 2011. Corresponding Editor: S. J. Schreiber.
1 Department of Ecology, Evolution and Marine Biology,
University of California, Santa Barbara, California 93106
USA.
2 University of Michigan, School of Natural Resources
and Environment, Ann Arbor, Michigan 48109 USA.
3 E-mail: [email protected]
In Carroll et al. (2011), we used a novel interpretation
of Chesson’s (2000) stabilizing and equalizing mechanisms of biodiversity to link the causes of diversity to its
consequences for biomass yield. We defined two
quantities, niche difference (ND) and relative fitness
difference (RFD), and showed how these jointly control
the relative yield total (RYT) in a simple version of
MacArthur’s consumer–resource model. Our work
exemplified how theory can link the maintenance of
biodiversity to its impacts on ecosystem functioning and
revealed that mechanisms that reduce fitness inequality
can have the same effect on yield as mechanisms that
increase a niche difference. We also demonstrated a
systematic deviation between ND and the complementarity effect (CE), a component of the method of
additive partitioning that has been widely calculated
for biodiversity experiments (AP; Loreau and Hector
2001). MacArthur’s model provides an explicit case in